New Approaches to H-Infinity Control I

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Author Index
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

Simultaneous Stabilization with Near Optimal H-Infinity Performance

Authors:

Daniel E. Miller, Tongwen Chen,

Volume: 1, Page 2722 Paper number 1560

Abstract:

In this paper we consider the use of linear periodically time-varying (LPTV) controllers for simultaneous stabilization and disturbance rejection. Here we consider the case in which the control signal does not appear directly in the output to be controlled and the disturbance does not appear directly in the measured output. We prove that for every finite set of such plants for which the high frequency gains (from the control signal to the measured output) satisfy a linear independence condition, we can design an LPTV controller which provides not only closed-loop stability, but also near optimal disturbance rejection in the H-infinity sense.

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Normalized H_(infinity) Controller Reduction with A Priori Bounds

Authors:

Haitham M.H. El-Zobaidi, Imad M. Jaimoukha, David J.N. Limebeer,

Volume: 1, Page 2728 Paper number 1276

Abstract:

This paper describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized H_(infinity) problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. When the approximation is performed on the controller generator, guaranteed a priori stability and performance bounds are obtained in terms of the synthesis Riccati equation solutions of the normalized H_(infinity) control problems.

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Further Order Reduction Of A Singular H_(infinity) Controller

Authors:

Takao Watanabe, Anton A. Stoorvogel,

Volume: 1, Page 2734 Paper number 2059

Abstract:

A new class of reduced-order controllers is obtained for the H_(infinity) problem. The reduced-order controller does not compromise the performance attained by the full-order controller. An algorithm for deriving the reduced-order H_(infinity) controller is presented in the case of continuous time. The reduction in order is related to unstable invariant zeros of the subsystem from disturbance inputs to measurement outputs. In the case where the subsystem has no infinite zeros, the resulting order of the H_(infinity) controller is lower than that of the existing reduced-order H_(infinity) controller designs which are based on reduced-order observer design. Furthermore, the mechanism of the controller order reduction is analyzed on the basis of the two-Riccati equation approach.

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From PI to H-Infinity Control in a Unified Framework

Authors:

Birgitta Kristiansson, Bengt Lennartson, Carl-Magnus Fransson,

Volume: 1, Page 2740 Paper number 2134

Abstract:

Based on a recently presented evaluation method, tuning rules are introduced and compared for a series of PID related controllers. For all of them, the integral gain and the high frequency gain (the parameters in a PI controller), are used as the main tuning parameters. As these directly correspond to well known properties of a control system, they are easy to handle for an operator. It is also shown that a well tuned PID controller augmented by a low pass filter, to increase the roll off rate, is quite competitive to a PID weighted H-inf controller, and superior to the common PI weighted H-inf controller.

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A Note on the Solution of a Class of BMIs for H-Infinity Problems

Authors:

Massimiliano Mattei,

Volume: 1, Page 2746 Paper number 9071

Abstract:

This note deals with the solution of a particular class of Bilinear Matrix Inequalities arising in the synthesis of H-infinity fixed-order controllers. It is well known that BMI optimisation problems are non convex and NP hard to solve. In this paper sufficient conditions are provided which allow to convert the controller design problem into a Linear Matrix Inequality feasibility problem.

CD009071.PDF (From Author)

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A New Design of Reduced-Order Controllers for Singular H-Infinity Control Problems Based on ARE Approach

Authors:

Xin Xin,

Volume: 1, Page 2748 Paper number 1543

Abstract:

The reduced-order controllers for singular H-infinity control problems with infinite zeros are studied via ARE (Algebraic Riccati Equation) approach in this paper. First, we analyze the relation between the eigenstructure corresponding to the infinite zeros and the parameterization of H-infinity controllers given in the descriptor form. Next, we propose a method to choose appropriately the free parameter in the parameterization for constructing the H-infinity controllers whose orders equal to the size of a reduced-order ARE involved in solvability conditions of the singular H-infinity control problems. The parameterization of the reduced-order H-infinity controllers is also discussed.

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Robust H-Infinity Control of Discrete-Time Linear Systems with Delayed State and Frobenius Norm-Bounded Uncertainties

Authors:

Li Yu, Furong Gao,

Volume: 1, Page 2754 Paper number 1056

Abstract:

The robust H_(infinity) control problem is considered in this paper for discrete-time linear systems with delayed state and subject to Frobenius norm-bounded parameter uncertainties, and attention is focused on the design of memoryless state feedback controllers. A design procedure for the robust H_(infinity) controllers is developed based on the linear matrix inequality (LMI) approach.

CD001056.PDF (From Author)

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